God I love, I first determine, on seeing grace, not works, produces salvation, forever redeeming, and he now empowers true living in Christ.

A problem from the old Monty Hall game show "Let's Make a Deal" has an answer that not many people get the first time they look at it. The contestant is shown three doors, behind one of which is a prize, and behind the other two no prize. The contestant picks a door, but before opening it the host selects one of the other two doors and opens it, revealing no prize. (This is of course always possible.) Then the host asks the contestant whether she wants to stick with the original door or switch to the third one. Is it better to stay or to switch?

Well, the probability that your first door hides the prize is 1/3, which remains the same if you see an empty door and do not switch. Therefore the probability that you were wrong in choosing that original door is 2/3, which is also the probability that between them, the other two doors conceal the prize. Now since the host always opens a door that does NOT have the prize, that 2/3 probability is no longer shared by 2 doors, but only one. Thus, if you switch the probability of winning is 2/3, but if you do not, it remains only 1/3.

The intuitive answer of 1/2 is wrong, though even some mathematicians are likely to disagree until they think carefully. By the way, no matter how many doors there are, it is always better to switch, though the difference gets smaller as the number of doors increase. [1/n versus (n-1)/n(n-2)] where n is the number of doors.

How can you distinguish among a mathematician, an engineer, and a physicist? Faced with identical situations, their responses differ.

A theatre curtain catches fire. The engineer grabs a fire extinguisher and a hose, covers curtain, stage, and audience with 300% more water and powder than necessary, but she does put the fire out.

The physicist runs to the front, pulls a thermometer from her pocket to measure the temperature of the flame, quickly determines the second and third derivatives of the function describing the pattern of fire in the curtain, looks up the material the curtain is made of in her handbook, does a fast calculation on her pocket computer, then pours 4.6736895 litres of water on the curtain, and the fire just goes out. There is a little wisp of smoke.

The mathematician walks to the front, examines the situation, and announces, "It is possible to put this fire out." Then she turns and walks away.

A Mathematician, a Biologist and a Physicist are sitting in a street
cafe watching people going in and coming out of the house on the
other side of the street. First they see two people going into the
house. Time passes. After a while they notice three persons coming
out of the house.

The Physicist says: "The measurement wasn't accurate."

The Biologist concludes: "They have reproduced."

The Mathematician says: "Now if another person enters the house,
it'll be empty again!"

---contributed by Linda L. Kerby

From the limerick page:

There once was a student from Trinity,
Tried to take the square root of infinity.
Whilst counting the digits
Was seized with the fidgets.
Gave up math and took up divinity.

Another version:

There once was a student at Trinity
Who computed the square of infinity.
But the number of digits
Gave him the fidgets
So he dropped math and took up divinity.
-- George Gamow in 1, 2. 3 Infinity

A logger cuts and sells a truckload of lumber for $100. His cost of production is four-fifths of that amount, and the taxes on the sale are 7%. What is his net profit?"

1970's (new math)

A logger exchanges a set L of lumber for a set M of money. The cardinality of M is 100. The set C of production costs contains 20 fewer items than does M. What is the cardinality of the set P of profits?

1980's

A logger sells a truckload of lumber for $100. His cost is $80 so his profit is $20. Circle the number 20.

1990's

A redneck logger massacres a beautiful stand of trees to make a profit of $20. Write an essay explaining how you feel about this ruthless capitalistic exploitation. Try to explain how the birds and the squirrels feel.

Though they are told of real mathematicians, I have anonymized the following stories, as they are partially apocryphal:

Smith and Jones went to a restaurant to have dinner and discuss theorems. While there, they got into an argument over whether the common person knew much mathematics--Smith on the positive side of the debate and Jones on the negative. Before dessert was served, Jones went off to the ladies' room. Smith, growling to herself and determined to win the argument, called the waitress over.
No more than a child, thought Smith. I shall have to resort to subterfuge. "Young lady, I want to play a trick on my colleague. Would you help me?"
"Certainly Ma'am. What can I do for you?"
"I'll ask you a question, and I want you to answer 'One third x cubed."
(hesitating) "One thir dex cubed."
The pair practiced to get it right, then Jones reappeared and the two ordered dessert. The argument resumed. After several minutes, the waitress returned with the pie and Smith was ready.
"I'll prove to you the common person knows a lot of mathematics," she said." (Turning to the waitress) "Young lady, what's the integral of the function x squared?"
Without hesitation, the waitress responded, "One third x cubed."
There was a brief pause during which a grin not unlike that of a shark suffused the countenance of Smith, then the young waitress added, in a cold voice, "plus a constant."

It was moving day for the family of Hamel, the famous and notoriously absent-minded mathematician. Since he could scarcely tie his own shoes, much less dress himself, his wife couldn't trust him to assist with anything so practical, so she sent him off to work as usual, but with a scrap of paper on which was written their new address, in hopes he could find his way home.

In the university cafeteria that day, inspiration came while eating the quiche. Hamel seized first his napkin then the paper place mat and began frantically scribbling equations. Partway through, he ran out of room. Desperate, he rummaged in his pocket and found a scrap, on which he finished his putative masterpiece. Alas, as all too often happens, the final result was disappointing, and he threw the lot in the trash on his way out (along with the stone cold quiche).

Returning home that night, he realized the curtains were missing from the windows. Suddenly, he remembered. Today had been moving day, and sure enough, he had forgotten. He fished in his pocket, but the paper was gone! What to do? He'd never live this one down.

Then he noticed a little girl sitting on the front step and had an inspiration. Kids always knew what was going on in the neighbourhood.

"Ahem, little girl, he enquired hopefully, "Do you know where the family who used to live in this house have moved to?"

The little girl smiled back fetchingly. "Of course. I'm to take you there. Mom said you'd forget, Dad. She sent me over here to bring you home."

The following is from Joel E. Cohen's article, taken from A Random Walk in Science:

Theorem: A horse has an infinite number of legs.
Proof (by intimidation): Horses have an even number of legs. Behind then have two legs and in front fore legs. This makes six legs, which is certainly an odd number of legs for a horse. But the only number that is both odd and even is infinity. Therefore horses have an infinite number of legs.

Literature provides us with some fascinating examples of mathematicians at play. One of the best is Edwin Abbott's Flatland (link below) which is simultaneously mathematical fiction and biting satire.

The answer: 3.1415'9265358979'32384626

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